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Question: The length of the latus-rectum of the ellipse \(5x^{2} + 9y^{2} = 45\)is...

The length of the latus-rectum of the ellipse 5x2+9y2=455x^{2} + 9y^{2} = 45is

A

5/4\sqrt{5}/4

B

5/2\sqrt{5}/2

C

5/35/3

D

10/310/3

Answer

10/310/3

Explanation

Solution

Here the ellipse is x29+y25=1\frac{x^{2}}{9} + \frac{y^{2}}{5} = 1

Here a2=9a^{2} = 9and b2=5b^{2} = 5. So, latus-rectum =2b2a= \frac{2b^{2}}{a}=2(5)3=103\frac{2(5)}{3} = \frac{10}{3}